{"id":128339,"date":"2021-09-16T14:51:33","date_gmt":"2021-09-16T09:21:33","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=128339"},"modified":"2021-09-16T14:51:37","modified_gmt":"2021-09-16T09:21:37","slug":"rd-sharma-class-10-solutions-chapter-14-exercise-14-4","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-14-exercise-14-4\/","title":{"rendered":"RD Sharma Class 10 Solutions Chapter 14 Co-ordinate Geometry Exercise 14.4 (Updated for 2021-22)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-128400\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-10-Solutions-Chapter-14-Exercise-14.4.jpg\" alt=\"RD Sharma Class 10 Solutions Chapter 14 Exercise 14.4\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-10-Solutions-Chapter-14-Exercise-14.4.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-10-Solutions-Chapter-14-Exercise-14.4-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Class 10 Solutions Chapter 14 Exercise 14.4:\u00a0<\/strong>The main topic of this exercise is section formula applications. The <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-for-maths\/\"><strong>RD Sharma Class 10 Solutions<\/strong><\/a> can be used to look out solutions to problems in any chapter of the book. Students can also use the links below to access the <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-14-co-ordinate-geometry\/\"><strong>RD Sharma Solutions for Class 10 Maths Chapter 14<\/strong><\/a> Co-ordinate Geometry Exercise 14.4 PDF.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69d4ef78645e8\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" 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href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-14-exercise-14-4\/#download-rd-sharma-class-10-solutions-chapter-14-exercise-144-free-pdf\" title=\"Download RD Sharma Class 10 Solutions Chapter 14 Exercise 14.4 Free PDF\">Download RD Sharma Class 10 Solutions Chapter 14 Exercise 14.4 Free PDF<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-14-exercise-14-4\/#access-answers-to-rd-sharma-solutions-class-10-maths-chapter-14-exercise-144-important-question-with-answers\" title=\"Access answers to RD Sharma Solutions Class 10 Maths Chapter 14 Exercise 14.4- Important Question with Answers\">Access answers to RD Sharma Solutions Class 10 Maths Chapter 14 Exercise 14.4- Important Question with Answers<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-14-exercise-14-4\/#faqs-on-rd-sharma-class-10-solutions-chapter-14-exercise-144\" title=\"FAQs on RD Sharma Class 10 Solutions Chapter 14 Exercise 14.4\">FAQs on RD Sharma Class 10 Solutions Chapter 14 Exercise 14.4<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-14-exercise-14-4\/#is-the-rd-sharma-class-10-solutions-chapter-14-exercise-144-available-on-the-kopykitab-website\" title=\"Is the RD Sharma Class 10 Solutions Chapter 14 Exercise 14.4 available on the Kopykitab website?\">Is the RD Sharma Class 10 Solutions Chapter 14 Exercise 14.4 available on the Kopykitab website?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-14-exercise-14-4\/#where-can-i-get-rd-sharma-class-10-solutions-chapter-14-exercise-144-free-pdf\" title=\"Where can I get RD Sharma Class 10 Solutions Chapter 14 Exercise 14.4 Free PDF?\">Where can I get RD Sharma Class 10 Solutions Chapter 14 Exercise 14.4 Free PDF?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-14-exercise-14-4\/#can-students-depend-on-the-rd-sharma-solutions-for-class-10-maths-chapter-14-exercise-144-for-their-exam-preparations-from-kopykitab\" title=\"Can students depend on the RD Sharma Solutions for Class 10 Maths Chapter 14 Exercise 14.4 for their exam preparations from Kopykitab?\">Can students depend on the RD Sharma Solutions for Class 10 Maths Chapter 14 Exercise 14.4 for their exam preparations from Kopykitab?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-class-10-solutions-chapter-14-exercise-144-free-pdf\"><\/span>Download RD Sharma Class 10 Solutions Chapter 14 Exercise 14.4 Free PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 800px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br \/><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Solution-Class-10-Chapter-14-Exercise-14.4.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Solution-Class-10-Chapter-14-Exercise-14.4.pdf\">RD Sharma Class 10 Solutions Chapter 14 Exercise 14.4<\/a><\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-answers-to-rd-sharma-solutions-class-10-maths-chapter-14-exercise-144-important-question-with-answers\"><\/span>Access answers to RD Sharma Solutions Class 10 Maths Chapter 14 Exercise 14.4- Important Question with Answers<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Question 1.<br \/>Find the centroid of the triangle whose vertices are :<br \/>(i) (1, 4), (-1, -1), (3, -2)<br \/>(ii) (-2, 3), (2, -1), (4, 0)<br \/>Solution:<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1746\/41830946765_5903435530_o.png\" alt=\"RD Sharma Class 10 Chapter 14 Co-Ordinate Geometry\" width=\"427\" height=\"203\" \/><\/p>\n<p>Question 2.<br \/>Two vertices of a triangle are (1, 2), (3, 5) and its centroid is at the origin. Find the Co-ordinates of the third vertex.<br \/>Solution:<br \/>Centroid of a triangle is O(0, 0) \u2026.(i)<br \/>Co-ordinates of two vertices of a \u2206ABC are A (1, 2) and B (3, 5)<br \/>Let the third vertex be (x, y)<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1742\/40920340570_0a04d6c919_o.png\" alt=\"RD Sharma Class 10 Chapter 14 Co-Ordinate Geometry\" width=\"638\" height=\"301\" \/><\/p>\n<p>Question 3.<br \/>Find the third vertex of a triangle, if two of its vertices are at (-3, 1) and (0, -2) and the centroid is at the origin.<br \/>Solution:<br \/>Let two vertices of a \u2206ABC be A (-3, 1) and B (0, -2) and third vertex C be (x, y)<br \/>Centroid of the \u2206ABC is O (0, 0)<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1745\/40920340890_07b9eab19d_o.png\" alt=\"Co-Ordinate Geometry Class 10 RD Sharma\" width=\"325\" height=\"471\" \/><\/p>\n<p>Question 4.<br \/>A (3, 2) and B (-2, 1) are two vertices of a triangle ABC whose centroid G has the coordinates (53\u00a0,\u00a0\u221213) . Find the coordinates of the third vertex C of the triangle. [CBSE 2004]<br \/>Solution:<br \/>A (3, 2) and B (-2, 1) are the two vertices of \u2206ABC whose centroid is G (53\u00a0,\u00a0\u221213)<br \/>Let third vertex C be (x, y)<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1726\/40920341150_bafbcdb6a9_o.png\" alt=\"Co-Ordinate Geometry Class 10 RD Sharma\" width=\"307\" height=\"391\" \/><\/p>\n<p>Question 5.<br \/>If (-2, 3), (4, -3) and (4, 5) are the mid-points of the sides of a triangle, find the co-ordinates of its centroid.<br \/>Solution:<br \/>In \u2206ABC, D, E and F are the mid-points of the sides BC, CA and AB respectively.<br \/>The co-ordinates of D are (-2, 3), of E are (4,-3) and of F are (4, 5)<br \/>Let the co-ordinates of A, B and C be (x<sub>1<\/sub>, y<sub>1<\/sub>), (x<sub>2<\/sub>, y<sub>2<\/sub>), (x<sub>3<\/sub>, y<sub>3<\/sub>) respectively<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1722\/40920341820_59d4dda6d2_o.png\" alt=\"RD Sharma Class 10 Solutions Co-Ordinate Geometry\" width=\"292\" height=\"325\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1746\/40920341340_746e326615_o.png\" alt=\"RD Sharma Class 10 Solutions Co-Ordinate Geometry Exercise 14.4\" width=\"361\" height=\"541\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1723\/40920341510_fa75677d7a_o.png\" alt=\"RD Sharma Class 10 Solutions Co-Ordinate Geometry\" width=\"347\" height=\"427\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1759\/40920341680_1354f05bfa_o.png\" alt=\"RD Sharma Class 10 Solutions Co-Ordinate Geometry Exercise 14.4\" width=\"304\" height=\"194\" \/><\/p>\n<p>Question 6.<br \/>Prove analytically that the line segment joining the middle points of two sides of a triangle is equal to half of the third side.<br \/>Solution:<br \/>In \u2206ABC,<br \/>D and E are the mid points of the sides AB and AC respectively<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1742\/40920342150_315f7bfeec_o.png\" alt=\"RD Sharma Class 10 Solutions Chapter 14 Co-Ordinate Geometry\" width=\"344\" height=\"581\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1744\/40920341970_7bef5a65e5_o.png\" alt=\"RD Sharma Class 10 Pdf Chapter 14 Co-Ordinate Geometry\" width=\"366\" height=\"370\" \/><\/p>\n<p>Question 7.<br \/>Prove that the lines joining the middle points of the opposite sides of a quadrilateral and the join of the middle points of its diagonals meet in a point and bisect one another.<br \/>Solution:<br \/>Let A (x<sub>1<\/sub>, y<sub>1<\/sub>), B (x<sub>2<\/sub>, y<sub>2<\/sub>), C (x<sub>3<\/sub>, y<sub>3<\/sub>) and D (x<sub>4<\/sub>, y<sub>4<\/sub>) be the vertices of quadrilateral ABCD<br \/>E and F are the mid points of side BC and AD respectively and EF is joined G and H are the mid points of diagonal AC and BD.<br \/>GH are joined<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1726\/40920342720_1abdfa277c_o.png\" alt=\"RD Sharma Class 10 Solutions Chapter 14 Co-Ordinate Geometry\" width=\"342\" height=\"321\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1752\/40920342390_b28f0f5e6f_o.png\" alt=\"RD Sharma Class 10 Pdf Chapter 14 Co-Ordinate Geometry\" width=\"348\" height=\"558\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1749\/40920342550_5ede72b4b8_o.png\" alt=\"RD Sharma Solutions Class 10 Chapter 14 Co-Ordinate Geometry\" width=\"349\" height=\"399\" \/><\/p>\n<p>Question 8.<br \/>If G be the centroid of a triangle ABC and P be any other point in the plane, prove that PA\u00b2 + PB\u00b2 + PC\u00b2 = GA\u00b2 + GB\u00b2 + GC\u00b2 + 3GP\u00b2.<br \/>Solution:<br \/>In AABC, G is the centroid of it Let P (h, x) is any point in the plane<br \/>Let co-ordinates of A are (x<sub>1<\/sub>, y<sub>1<\/sub>) of B are (x<sub>2<\/sub>, y<sub>2<\/sub>) and of C are (x<sub>3<\/sub>, y<sub>3<\/sub>)<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1751\/41830948785_7eb554b442_o.png\" alt=\"Learncbse.In Class 10 Chapter 14 Co-Ordinate Geometry\" width=\"246\" height=\"214\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1756\/41830948475_8618f639cc_o.png\" alt=\"Learncbse.In Class 10 Chapter 14 Co-Ordinate Geometry\" width=\"719\" height=\"417\" \/><br \/>Hence proved.<\/p>\n<p>Question 9.<br \/>If G be the centroid of a triangle ABC, prove that AB\u00b2 + BC\u00b2 + CA\u00b2 = 3 (GA\u00b2 + GB\u00b2 + GC\u00b2)<br \/>Solution:<br \/>Let the co-ordinates of the vertices of \u2206ABC be A (x<sub>1<\/sub>, y<sub>1<\/sub>), B (x<sub>2<\/sub>, y<sub>2<\/sub>), C (x<sub>3<\/sub>, y<sub>3<\/sub>) and let G be the centroid of the triangle<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1732\/40920343850_54a72e0c6a_o.png\" alt=\"Class 10 RD Sharma Solutions Chapter 14 Co-Ordinate Geometry\" width=\"585\" height=\"359\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1742\/41830948945_57a3934d94_o.png\" alt=\"RD Sharma Class 10 Pdf Free Download Full Book Chapter 14 Co-Ordinate Geometry \" width=\"589\" height=\"423\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1748\/40920343710_af2c1f4348_o.png\" alt=\"Class 10 RD Sharma Solutions Chapter 14 Co-Ordinate Geometry\" width=\"546\" height=\"136\" \/><br \/>Hence proved.<\/p>\n<p>Question 10.<br \/>In the figure, a right triangle BOA is given. C is the mid-point of the hypotenuse AB. Show that it is equidistant from the vertices O, A and B.<br \/>Solution:<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1748\/40920344060_ce66d3a91f_o.png\" alt=\"RD Sharma Class 10 Solution Chapter 14 Co-Ordinate Geometry\" width=\"220\" height=\"211\" \/><br \/>In right \u2206OAB, co-ordinates of O are (0, 0) of A are (2a, 0) and of B are (0, 2b)<br \/>C is the mid-point of AB<br \/>Co-ordinates of C will be<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1732\/40920343960_b09a1239f8_o.png\" alt=\"RD Sharma Class 10 Solution Chapter 14 Co-Ordinate Geometry\" width=\"338\" height=\"308\" \/><br \/>We see that CO = CA = CB<br \/>Hence C is equidistant from the vertices O, A and B.<br \/>Hence proved.<\/p>\n<p>We have provided complete details of RD Sharma Class 10 Solutions Chapter 14 Exercise 14.4. If you have any queries related to <a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\"><strong>CBSE<\/strong><\/a>\u00a0Class 10, feel free to ask us in the comment section below.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"faqs-on-rd-sharma-class-10-solutions-chapter-14-exercise-144\"><\/span>FAQs on RD Sharma Class 10 Solutions Chapter 14 Exercise 14.4<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1631771888823\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"is-the-rd-sharma-class-10-solutions-chapter-14-exercise-144-available-on-the-kopykitab-website\"><\/span>Is the RD Sharma Class 10 Solutions Chapter 14 Exercise 14.4 available on the Kopykitab website?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, the PDFs of RD Sharma Class 10 Solutions Chapter 14 Exercise 14.4 are available. These solutions are created in a unique method by Kopykitab\u2019s expert faculty.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1631772015754\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"where-can-i-get-rd-sharma-class-10-solutions-chapter-14-exercise-144-free-pdf\"><\/span>Where can I get RD Sharma Class 10 Solutions Chapter 14 Exercise 14.4 Free PDF?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can get RD Sharma Class 10 Solutions Chapter 14 Exercise 14.4 Free PDF from the above article.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1631772088203\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"can-students-depend-on-the-rd-sharma-solutions-for-class-10-maths-chapter-14-exercise-144-for-their-exam-preparations-from-kopykitab\"><\/span>Can students depend on the RD Sharma Solutions for Class 10 Maths Chapter 14 Exercise 14.4 for their exam preparations from Kopykitab?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, students can trust the RD Sharma Class 10 Solutions Chapter 14 Exercise 14.4 on the Kopykitab website since subject matter experts have created the solutions in accordance with the most recent CBSE guidelines and exam patterns. Furthermore, students can swiftly study the main concepts of the chapters in both online and offline formats at any time and from anywhere.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Class 10 Solutions Chapter 14 Exercise 14.4:\u00a0The main topic of this exercise is section formula applications. The RD Sharma Class 10 Solutions can be used to look out solutions to problems in any chapter of the book. Students can also use the links below to access the RD Sharma Solutions for Class 10 &#8230; <a title=\"RD Sharma Class 10 Solutions Chapter 14 Co-ordinate Geometry Exercise 14.4 (Updated for 2021-22)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-14-exercise-14-4\/\" aria-label=\"More on RD Sharma Class 10 Solutions Chapter 14 Co-ordinate Geometry Exercise 14.4 (Updated for 2021-22)\">Read more<\/a><\/p>\n","protected":false},"author":238,"featured_media":128400,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73411,2985,73410],"tags":[3243,9206,73520,4388],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/128339"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/238"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=128339"}],"version-history":[{"count":5,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/128339\/revisions"}],"predecessor-version":[{"id":128427,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/128339\/revisions\/128427"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/128400"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=128339"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=128339"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=128339"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}